A few thoughts on your headaches - as you've noted, dehydration is the first suspect, and you may need more water than you think.

Do you get your heart beating fast and hard suddenly? That might cause something in your temple to tighten up (not a medical answer, but I know a lot about headaches, from experience). I've been treated with caffeine (of all things!) for that - if you have coffee before hand, it may help with constriction issues. Caffeine can also cause headaches, so you can't win.

Finally, are you tensing muscles? Check in with each muscle ("how are you doing left shoulder? Feeling Ok?") - use your running / jogging time to feel all the parts of your body, you may be adding tension where you don't know it.

Of course, headaches can be a sign of something serious, you should be sure to seek appropriate medical care...